This paper is concerned with the mixed boundary value problems of an infinite plate with a square hole into which a smooth rigid square plug with rounded corners is simply inserted. Since the infinite plate is subjected to a uniaxial tension at infinity, gaps are produced along the boundary between the inserted plug and the hole. The contact pressure between the inserted plug and the hole is expressed in a convergent series, so that the stress and displacement along the boundary can be numerically analyzed by the point matching method. Using the numerical results for the shape of a square hole with rounded corners, the influence of the interference is shown with the stress around a square hole.